Induction—please help!

My husband and I plan for me to be induced at 39 weeks because he is in the military and called for mandatory duty 4 days before my due date. My question is, how long after you were induced did your baby come? Since he will have to leave when I would be 39 weeks and 3 days, I am worried I will be induced at 39 weeks and be in labor for multiple days and still have him miss the birth. Does this happen, or do they usually come right away when induced? Thanks!